隨著航空產業科技的快速進步，無人飛行系統已成為現今航空產業熱門話題，無人機種類繁多，其中以四旋翼之機動性能最為卓越，因此，本文選擇四旋翼為研究主題。
本文提出利用勢能場(Potential Field)來達到路徑規劃和障礙迴避之目標，並將其應用在四旋翼上。勢能場由吸引勢能與排斥勢能結合而成，基本概念是利用虛擬的位能場，使四旋翼朝目標前進。目標位置有一個虛擬之吸引力，障礙物位置有一個虛擬之排斥力，當接近障礙物時，四旋翼會因為虛擬之排斥力而進行迴避障礙物之動作；反之，四旋翼會因為虛擬吸引力而飛行至目標。
本文構想為同時控制多台四旋翼沿著預先規劃的路徑飛行，不僅要能遵循特定軌跡且多台四旋翼隊形亦須保持穩定。若只單純依靠感測器迴避障礙會有一定的風險。最終達到避免飛行中之四旋翼機群因距離或時間延遲導致意外發生。從本文模擬結果可以發現，經由路徑規劃之妥善執行可達到完成飛行任務之目標。

With the rapid developing of science and technology, the unmanned aircraft system has become a hot topic in the aeronautical industry. Quadcopter is a common use de-vice in all kinds of unmanned aerial vehicles. Therefore, the quadcopter is selected for this topic.Potential field is proposed for route planning and obstacle avoidance in this research, which is applied in quadcopter. The potential field is combined with the at-tractive and repulsive potential energy. We use a virtual potential field to drive the quadcopter. We assumed the goal has a virtual attractive force while the obstacle has a virtual repulsive force. While the quadcopter is moving to obstacles, it will bypass the obstacles because of the virtual repulsive force. In other words, the quadcopter will follow the path to achieve the goal because of the virtual attractive force.Following the pre-planned route, the multiple quadcopters not only fly around the side to pass the obstacles but also keep the distance between each other. Therefore, the purpose of this paper is to avoid the distance and delay problem in the team of the quadcopters. As a result, the flying mission can be achieve through the route planning and obstacle avoidance.

[1] YUAN, Deming, et al. Distributed dual averaging method for multi-agent optimization with quantized communication. Systems & Control Letters, 2012, 61.11: 1053-1061.
[2] WANG, Yinqiu, et al. Consensus algorithm for multiple quadrotor systems under fixed and switching topologies. Journal of Systems Engineering and Electronics, 2013, 24.5: 818-827.
[3] 王紅雨, 等. 四旋翼飛行器建模及位置跟踪控制. 中國慣性技術學報, 2012, 20.4: 455-458.
[4] ABBAS, Rabah; WU, Qinghe. Formation tracking for multiple quadrotor based on sliding mode and fixed communication topology. In: Intelligent Human-Machine Systems and Cybernetics (IHMSC), 2013 5th International Conference on. IEEE, 2013. p. 233-238.
[5] GARCIA-DELGADO, L., et al. Quad-rotors formation based on potential functions with obstacle avoidance. IET Control Theory & Applications, 2012, 6.12: 1787-1802
[6] MERCADO, D. A.; CASTRO, R.; LOZANO, Rogelio. Quadrotors flight formation control using a leader-follower approach. In: Control Conference (ECC), 2013 European. IEEE, 2013. p. 3858-3863.
[7] WASLANDER, Steven Lake, et al. Multi-agent quadrotor testbed control design: Integral sliding mode vs. reinforcement learning. In: Intelligent Robots and Systems, 2005.(IROS 2005). 2005 IEEE/RSJ International Conference on. IEEE, 2005. p. 3712-3717.
[8] CHOI, Young-Cheol; AHN, Hyo-Sung. Nonlinear control of quadrotor for point tracking: Actual implementation and experimental tests. IEEE/ASME transactions on mechatronics, 2015, 20.3: 1179-1192.
[9] SATICI, Aykut C.; POONAWALA, Hasan; SPONG, Mark W. Robust optimal control of quadrotor UAVs. IEEE Access, 2013, 1: 79-93.
[10] CABECINHAS, David; CUNHA, Rita; SILVESTRE, Carlos. A nonlinear quadrotor trajectory tracking controller with disturbance rejection. Control Engineering Practice, 2014, 26: 1-10.
[11] LEE, DongBin, et al. Output feedback tracking control of an underactuated quad-rotor UAV. In: American Control Conference, 2007. ACC'07. IEEE, 2007. p. 1775-1780.
[12] DE JESUS RUBIO, Jose, et al. Comparison of two quadrotor dynamic models. IEEE Latin America Transactions, 2014, 12.4: 531-537.
[13] ALEXIS, Kostas; NIKOLAKOPOULOS, George; TZES, Anthony. Model predictive quadrotor control: attitude, altitude and position experimental studies. IET Control Theory & Applications, 2012, 6.12: 1812-1827.
[14] LAFLEUR, Karl, et al. Quadcopter control in three-dimensional space using a noninvasive motor imagery-based brain–computer interface. Journal of neural engineering, 2013, 10.4: 046003
[15] LUUKKONEN, Teppo. Modelling and control of quadcopter. Independent research project in applied mathematics, Espoo, 2011.
[16] SA, Inkyu; CORKE, Peter. System identification, estimation and control for a cost effective open-source quadcopter. In: Robotics and automation (icra), 2012 ieee international conference on. IEEE, 2012. p. 2202-2209.
[17] MA'SUM, M. Anwar, et al. Autonomous quadcopter swarm robots for object localization and tracking. In: Micro-NanoMechatronics and Human Science (MHS), 2013 International Symposium on. IEEE, 2013. p. 1-6.
[18] KENDALL, Alex G.; SALVAPANTULA, Nishaad N.; STOL, Karl A. On-board object tracking control of a quadcopter with monocular vision. In: Unmanned Aircraft Systems (ICUAS), 2014 International Conference on. IEEE, 2014. p. 404-411.
[19] REMES, Bart, et al. Paparazzi: how to make a swarm of parrot ar drones fly autonomously based on gps. In: International Micro Air Vehicle Conference and Flight Competition (IMAV2013). 2013. p. 17-20.
[20] CHAUMETTE, Serge, et al. Carus, an operational retasking application for a swarm of autonomous uavs: First return on experience. In: MILITARY COMMUNICATIONS CONFERENCE, 2011-MILCOM 2011. IEEE, 2011. p. 2003-2010.
[21] GE, Shuzhi Sam; CUI, Yun J. Dynamic motion planning for mobile robots using potential field method. Autonomous robots, 2002, 13.3: 207-222.
[22] TANG, Lei, et al. A novel potential field method for obstacle avoidance and path planning of mobile robot. In: Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on. IEEE, 2010. p. 633-637.
[23] WANG, Xiao-Dong, et al. A three-dimensional numerical modeling of thermoelectric device with consideration of coupling of temperature field and electric potential field. Energy, 2012, 47.1: 488-497.
[24] YU, Zhen-zhong, et al. Mobile robot path planning based on improved artificial potential field method. Harbin Gongye Daxue Xuebao(Journal of Harbin Institute of Technology), 2011, 43.1: 50-55.
[25] MONTIEL, Oscar; OROZCO-ROSAS, Ulises; SEPÚLVEDA, Roberto. Path planning for mobile robots using Bacterial Potential Field for avoiding static and dynamic obstacles. Expert Systems with Applications, 2015, 42.12: 5177-5191.
[26] PANEQUE-GÁLVEZ, Jaime, et al. Small drones for community-based forest monitoring: An assessment of their feasibility and potential in tropical areas. Forests, 2014, 5.6: 1481-1507.
[27] PIERRE, Djamalladine Mahamat; ZAKARIA, Nordin; PAL, Anindya Jyoti. Master-slave parallel vector-evaluated genetic algorithm for unmanned aerial vehicle's path planning. In: Hybrid Intelligent Systems (HIS), 2011 11th International Conference on. IEEE, 2011. p. 517-521.
[28] BARNES, Laura; FIELDS, MaryAnne; VALAVANIS, Kimon. Unmanned ground vehicle swarm formation control using potential fields. In: Control & Automation, 2007. MED'07. Mediterranean Conference on. IEEE, 2007. p. 1-8.
[29] SASKA, Martin, et al. Robot path planning using particle swarm optimization of Ferguson splines. In: Emerging Technologies and Factory Automation, 2006. ETFA'06. IEEE Conference on. IEEE, 2006. p. 833-839.
[30] DOS SANTOS COELHO, Leandro; MARIANI, Viviana Cocco. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Conversion and Management, 2008, 49.11: 3080-3085.